On large delays in multi-server queues with heavy tails

Foss, Sergey and Korshunov, Dmitry (2012) On large delays in multi-server queues with heavy tails. Mathematics of Operations Research, 37 (2). pp. 201-218. ISSN 0364-765X

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We present upper and lower bounds for the tail distribution of the stationary waiting time D in the stable GI/GI/s first-come first-served (FCFS) queue. These bounds depend on the value of the traffic load ρ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a “principle of s − k big jumps” in this case (here k is the integer part of ρ), which gives the most probable way for the stationary waiting time to be large. Another corollary of the bounds obtained is to provide a new proof of necessity and sufficiency of conditions for the existence of moments of the stationary waiting time.

Item Type: Journal Article
Journal or Publication Title: Mathematics of Operations Research
Uncontrolled Keywords: /dk/atira/pure/subjectarea/aacsb/disciplinebasedresearch
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 76867
Deposited By: ep_importer_pure
Deposited On: 25 Nov 2015 09:22
Refereed?: Yes
Published?: Published
Last Modified: 07 Jan 2020 04:39
URI: https://eprints.lancs.ac.uk/id/eprint/76867

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